The 'Goose' is run by Peninsula Airways, and is the only way to fly in or out of Akutan. It runs from Dutch Harbor to the dock of Akutan. This is perhaps the most beautiful plane flight I've ever been on. It is a seaplane, and thus runs low to the ground, perhaps only 1000-1200 feet up. You carve along the coast between islands, then across Akutan island, weaving through the hills until you reach the bay where Akutan sits. You splash down and taxi towards the ramp that leads up out of the water. It is a strange feeling going from flying to floating in one moment. Beautiful scenery all around, and the touch down/take off on the water is indescribable. Almost worth the cost of the ticket in itself.
Due to the low altitude of flying, this is a very precarious plane flight. Make sure to give yourself buffer time if you're connecting on the return leg; low-lying fog and clouds can delay this plane for hours, even days. In July when I was trying to get to Akutan, it took 3 days before the weather cleared. In September, it was late by a day. Just be warned, and be flexible.
Departure times from Dutch Harbor: 11:00am, 4:30pm
Flight time: 20 minutes
Cost (round-trip): ~$230
I guess the monthly (during the summer) ferry stops there briefly but the usual ways to get to Akutan are on the goose (a Grumman Goose, circa 1950, is an amphibious plane that can land on wheels on a runway or, as there is no runway in Akutan, can land on it's belly in the water). Here it's wheeling out of the water to it's landing pad in front of the brand new church built largely by the owner of the Trident plant situated between the village and the plant.